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Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Contaminants and Errors01:16

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Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
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Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Semi-Supervised Minimum Error Entropy Principle with Distributed Method.

Baobin Wang1, Ting Hu2

  • 1School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

The minimum error entropy principle (MEE) offers robust regression against non-Gaussian noise. Semi-supervised learning with unlabeled data improves distributed MEE, achieving minimax optimal performance with more machines.

Keywords:
MEE algorithmdistributed methodgradient descentinformation theoretical learningreproducing kernel Hilbert spacessemi-supervised approach

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Area of Science:

  • Machine Learning
  • Statistical Signal Processing
  • Optimization Theory

Background:

  • Classical least squares methods are sensitive to non-Gaussian noise.
  • Minimum Error Entropy (MEE) principle provides a robust alternative.
  • Distributed and semi-supervised learning paradigms offer potential for enhanced performance.

Purpose of the Study:

  • To investigate the gradient descent algorithm for MEE within a semi-supervised and distributed framework.
  • To demonstrate the benefits of incorporating unlabeled data in distributed MEE.
  • To establish theoretical guarantees for the performance of the proposed algorithm.

Main Methods:

  • Developed a distributed gradient descent algorithm based on the MEE principle.
  • Incorporated unlabeled data using a semi-supervised learning approach.
  • Analyzed the algorithm's convergence and error bounds.

Main Results:

  • The integration of unlabeled data significantly enhances the learning capability of the distributed MEE algorithm.
  • The proposed distributed gradient descent MEE algorithm achieves minimax optimal mean squared error for regression.
  • Performance improvement is contingent on the polynomial scaling of local machines with the total data size.

Conclusions:

  • Semi-supervised learning is a powerful technique for improving distributed MEE algorithms.
  • The MEE principle, when combined with distributed and semi-supervised methods, offers a robust and efficient approach to regression.
  • Theoretical analysis confirms the minimax optimality of the proposed method under specific scaling conditions.